It depends upon the content of the letter.
Just "Thanks," alone can sound off key if there is nothing obvious for which thanks to the reader is warranted, or too light-hearted when providing serious information. "Sincerely," is (to me) taking on an emotional component of a personal relationship to emphasize feelings. In professional communications no such intensifier is necessary or desired. It can look false and amateurish, because in many professional communications insincerity is assumed.
The most common endings I see are neutral ("Regards,") to apply to any situation, from informing somebody they are terminated to informing somebody they are hired.
Another common exit that works is "Thank you for XXXX," as in,
Thank you for your interest,
Thank you for your time,
Thank you for considering us,
And so on.
In general, the rule in professional communications is to remain very neutral or understated, and avoid (in the letter, salutation, or closing) exaggeration that sounds very emotional. Nobody is angry, they are "disappointed". Nobody is joyful, they are "pleased." Professional communications are generally even-keeled and tilt only a modest amount toward positive or negative tone. Even terrifying or horrific news is this way: "We regret to inform you..."
We stick to the facts, "look forward to" some event, "Hope to hear from you soon," etc. Find ways to keep effusive emotions out of it. If emotion seems to be warranted, search the online thesaurus for a synonym that understates your feelings (or if you can't put a finger on what you feel, try an antonym to the opposite of what you feel, or an antonym to something you definitely do not feel).